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Arc-Disjoint Cycles and Feedback Arc Sets

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Abstract

Isaak posed the following problem. Suppose T is a tournament having a minimum feedback arc set, which induces an acyclic digraph with a hamiltonian path. Is it true that the maximum number of arc-disjoint cycles in T equals the cardinality of minimum feedback arc set of T? We prove that the answer to the problem is in the negative.

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